Android devices are commonly known to boycott power on at times when the the Operating System or firmware gets corrupted. Hard reset is a known quick fix for the power on issue. You can try and hard reset the device by doing the following.
1. Press and hold down Volume Up+Power button (You need to do this while the phone is off).
2. The phone will restart
Please do comment under this selfsame question if you Alcatel One Touch is not Android based (including it particular model number) and we'll try and assist further.